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2017•arXiv (Cornell University)Open access

Enneper representation of minimal surfaces in the three-dimensional\n Lorentz-Minkowski space

Irene I. Onnis, Adriana A. Cintra

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Abstract

In this paper, we will give an Enneper-type representation for spacelike and\ntimelike minimal surfaces in the Lorentz-Minkowski space $L^{3}$, using the\ncomplex and the paracomplex analysis (respectively). Then, we exhibit various\nexamples of minimal surfaces in $L^{3}$ constructed via the Enneper\nrepresentation formula, that it is equivalent to the Weierstrass representation\nobtained by Kobayashi (for spacelike immersions) and by Konderak (for the\ntimelike ones).\n

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In this paper, we will give an Enneper-type representation for spacelike and\ntimelike minimal surfaces in the Lorentz-Minkowski space $L^{3}$, using the\ncomplex and the paracomplex analysis (respectively). Then, we exhibit various\nexamples of minimal surfaces in $L^{3}$ constructed via the Enneper\nrepresentation formula, that it is equivalent to the Weierstrass representation\nobtained by Kobayashi (for spacelike immersions) and by Konderak (for the\ntimelike ones).\n

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Available abstract

In this paper, we will give an Enneper-type representation for spacelike and\ntimelike minimal surfaces in the Lorentz-Minkowski space $L^{3}$, using the\ncomplex and the paracomplex analysis (respectively). Then, we exhibit various\nexamples of minimal surfaces in $L^{3}$ constructed via the Enneper\nrepresentation formula, that it is equivalent to the Weierstrass representation\nobtained by Kobayashi (for spacelike immersions) and by Konderak (for the\ntimelike ones).\n

Key concepts: Minkowski space, Lorentz transformation, Representation (politics), Space (punctuation), Mathematics, Pure mathematics, Mathematical analysis, Mathematical physics

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